期刊
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
卷 20, 期 4, 页码 868-894出版社
SPRINGERNATURE
DOI: 10.1515/fca-2017-0046
关键词
time-fractional telegraph equation; fundamental solution; Caputo fractional derivative; multivariate Mittag-Leffler functions; H-function of two variables; double Mellin-Barnes type integrals
资金
- Portuguese funds through CIDMA - Center for Research and Development in Mathematics and Applications
- Portuguese Foundation for Science and Technology (FCT-Fundacao para a Ciencia e a Tecnologia) [UID/MAT/ 0416/2013]
- FCT [IF/00271/2014]
In this paper we study the fundamental solution (FS) of the multidimensional time-fractional telegraph equation where the time-fractional derivatives of orders alpha is an element of] 0, 1] and beta alpha] 1, 2] are in the Caputo sense. Using the Fourier transform we obtain an integral representation of the FS in the Fourier domain expressed in terms of a multivariate Mittag-Leffler function. The Fourier inversion leads to a double Mellin-Barnes type integral representation and consequently to a H-function of two variables. An explicit series representation of the FS, depending on the parity of the dimension, is also obtained. As an application, we study a telegraph process with Brownian time. Finally, we present some moments of integer order of the FS, and some plots of the FS for some particular values of the dimension and of the fractional parameters alpha and beta.
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